{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Results\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "# We run the following SciPy and NumPy code in [1] \n",
    "# and generate the plots mentioned above using Matplotlib \n",
    "\n",
    "# load the UN dataset transformed to float with 4 numeric columns, \n",
    "# lifeMale,lifeFemale,infantMortality and GDPperCapita\n",
    "\n",
    "fName = ('../datasets/UN4col.csv')\n",
    "fp = open(fName)\n",
    "X = np.loadtxt(fp)\n",
    "fp.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.cluster.vq import kmeans,vq\n",
    "from scipy.spatial.distance import cdist\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "##### cluster data into K=1..10 clusters #####\n",
    "#K, KM, centroids,D_k,cIdx,dist,avgWithinSS = kmeans.run_kmeans(X,10)\n",
    "\n",
    "K = range(1,10)\n",
    "\n",
    "  # scipy.cluster.vq.kmeans\n",
    "KM = [kmeans(X,k) for k in K] # apply kmeans 1 to 10\n",
    "centroids = [cent for (cent,var) in KM]   # cluster centroids\n",
    "\n",
    "D_k = [cdist(X, cent, 'euclidean') for cent in centroids]\n",
    "\n",
    "cIdx = [np.argmin(D,axis=1) for D in D_k]\n",
    "dist = [np.min(D,axis=1) for D in D_k]\n",
    "avgWithinSS = [sum(d)/X.shape[0] for d in dist]  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYsAAAEVCAYAAAARjMm4AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngg==\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kIdx = 2\n",
    "# plot elbow curve\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "ax.plot(K, avgWithinSS, 'b*-')\n",
    "ax.plot(K[kIdx], avgWithinSS[kIdx], marker='o', markersize=12, \n",
    "      markeredgewidth=2, markeredgecolor='r', markerfacecolor='None')\n",
    "plt.grid(True)\n",
    "plt.xlabel('Number of clusters')\n",
    "plt.ylabel('Average within-cluster sum of squares')\n",
    "tt = plt.title('Elbow for K-Means clustering')  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So we see that a good K to use in our model would be 3.\n",
    "We now use the KMeans modeling software to fit clusters to our data and then plot how the software has clustered our data.\n",
    "In this case we look at how the data cluster when we plot Infant Mortality against GDP."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.cluster import KMeans\n",
    "km = KMeans(3, init='k-means++') # initialize\n",
    "km.fit(X)\n",
    "c = km.predict(X) # classify into three clusters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZAAAAEXCAYAAACDChKsAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nIBKJRCJxCKlAJBKJROIQ/x/k7BNVgFPFrgAAAABJRU5ErkJggg==\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# see the code in helper library kmeans.py\n",
    "# it wraps a number of variables and maps integers to categoriy labels\n",
    "# this wrapper makes it easy to interact with this code and try other variables\n",
    "# as we see below in the next plot\n",
    "import kmeans as mykm\n",
    "(pl0,pl1,pl2) = mykm.plot_clusters(X,c,3,2) # column 3 GDP, vs column 2 infant mortality. Note indexing is 0 based"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we see some patterns, obvious in retrospect.  The countries with GDP (in US Dollars) below 10K have rapidly rising infant mortality as GDP drops. On the other hand as GDP rises we see rapidly decreasing infant mortality, which is as we know, a correlate of financial prosperity, i.e. high GDP.\n",
    "\n",
    "We also see 3 clusters which we can informally call, the underdeveloped, the developing and the developed countries, based on, respectively, GDP (in US Dollars) below 10K, between 10K and 20K and finally greater than 20K.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What would happen if we tried other dimensions to cluster on, say lifeMale and GDPperCapita.\n",
    "Let's see."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYsAAAEXCAYAAABcRGizAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTkSuQmCC\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "(pl0,pl1,pl2) = mykm.plot_clusters(X,c,3,0,False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And similarly with lifeFemale vs GDPperCapita.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYsAAAEXCAYAAABcRGizAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQohV1FgQQgix6i95zYlxZuL5gQAAAABJRU5ErkJggg==\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "(pl0,pl1,pl2) = mykm.plot_clusters(X,c,3,1,False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In both the last two cases we see an opposite trend to infant mortality, where life expectancy rises rapidly as GDP grows, but drop precipitously even to below 40 yrs for countries with the lowest GDP."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sections of code above are taken from a StackOverflow discussion [1].  \n",
    "Authorship of these segments is due to user Amro [2] on StackOverflow.  \n",
    "The discussion [1] has greater detail and more extensive examples and the reader is referred there for more depth."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise\n",
    "* Follow the link to the StackOverflow discussion [1].  \n",
    "* Look at the handwriting recognition dataset.  \n",
    "* Import it and run the code in the rest of the discussion.  \n",
    "* Do you get similar results?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##References\n",
    "[1] http://stackoverflow.com/questions/6645895/calculating-the-percentage-of-variance-measure-for-k-means  \n",
    "[2] http://stackoverflow.com/users/97160/amro"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       "    @font-face {\n",
       "        font-family: \"Computer Modern\";\n",
       "        src: url('http://mirrors.ctan.org/fonts/cm-unicode/fonts/otf/cmunss.otf');\n",
       "    }\n",
       "    div.cell{\n",
       "        width:800px;\n",
       "        margin-left:auto;\n",
       "        margin-right:auto;\n",
       "    }\n",
       "    h1 {\n",
       "        font-family: \"Charis SIL\", Palatino, serif;\n",
       "    }\n",
       "    h4{\n",
       "        margin-top:12px;\n",
       "        margin-bottom: 3px;\n",
       "       }\n",
       "    div.text_cell_render{\n",
       "        font-family: Computer Modern, \"Helvetica Neue\", Arial, Helvetica, Geneva, sans-serif;\n",
       "        line-height: 145%;\n",
       "        font-size: 120%;\n",
       "        width:800px;\n",
       "        margin-left:auto;\n",
       "        margin-right:auto;\n",
       "    }\n",
       "    .CodeMirror{\n",
       "            font-family: \"Source Code Pro\", source-code-pro,Consolas, monospace;\n",
       "    }\n",
       "    .prompt{\n",
       "        display: None;\n",
       "    }\n",
       "    .text_cell_render h5 {\n",
       "        font-weight: 300;\n",
       "        font-size: 16pt;\n",
       "        color: #4057A1;\n",
       "        font-style: italic;\n",
       "        margin-bottom: .5em;\n",
       "        margin-top: 0.5em;\n",
       "        display: block;\n",
       "    }\n",
       "    \n",
       "    .warning{\n",
       "        color: rgb( 240, 20, 20 )\n",
       "        }\n",
       "</style>\n",
       "<script>\n",
       "    MathJax.Hub.Config({\n",
       "                        TeX: {\n",
       "                           extensions: [\"AMSmath.js\"]\n",
       "                           },\n",
       "                tex2jax: {\n",
       "                    inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
       "                    displayMath: [ ['$$','$$'], [\"\\\\[\",\"\\\\]\"] ]\n",
       "                },\n",
       "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
       "                \"HTML-CSS\": {\n",
       "                    styles: {'.MathJax_Display': {\"margin\": 4}}\n",
       "                }\n",
       "        });\n",
       "</script>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML at 0x10b49c550>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.core.display import HTML\n",
    "def css_styling():\n",
    "    styles = open(\"../styles/custom.css\", \"r\").read()\n",
    "    return HTML(styles)\n",
    "css_styling()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
